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Research Methods, Design,
and Analysis
Twelfth Edition
CHAPTER
15
Inferential Statistics
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Inferential Statistics
• Inferential statistics
– using sample data to make inferences about
populations
• Statistic
– a numerical index based on sample data
• Parameter
– a numerical characteristic of a population
• Two major divisions
– estimation
– hypothesis testing
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Sampling Distributions
• Sampling distribution
– the theoretical probability distribution of the values of a statistic that
would result if you selected all possible samples of a particular size from
a population
• Sampling distribution of the mean
– the theoretical probability distribution of the means of all possible
samples of a particular size selected from a population
– how its done
1. draw a random sample of a certain size from the population, calculate and
write down the value of the sample mean
2. draw another random sample (of the same size), calculate and write down
the value of this sample mean
3. continue this process an infinite number of times or until all possible samples
of a particular size (e.g., 30 people per sample) have been recorded
4. then display all of the sample means obtained. If you construct a line graph of
all of these sample means, you will have a depiction of your sampling
distribution of the mean
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Sampling Distributions
• Standard error
– the standard deviation of a sampling distribution
• A sampling distribution can be made for any
sample statistic
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Hypothesis Testing
• The branch of inferential statistics focused on determining when
the null hypothesis can or cannot be rejected in favor of the
alternative hypothesis
• The process of testing a predicted relationship or hypothesis by
making observations and then comparing the observed facts
with the hypothesis or predicted relationship
• Null hypothesis
– a statement regarding the population parameter
– no relationship exists between the independent and dependent variables
– researcher hopes to “nullify”
• Alternative hypothesis
– states that there is a relationship between independent and dependent
variables
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Hypothesis Testing
•
Steps of hypothesis testing
1. state the null and alternative hypotheses

both are stated in population parameters
–
–
e.g., null hypothesis: H0: μM = μF
e.g., alternative hypothesis: H1: μM ≠ μF
2. begin by assuming that the null hypothesis is true (that the
independent variable has no effect)

the researcher wants to reject H0 and accepts H1
3. determine the standard for rejecting the null hypothesis


i.e., identify the level of significance
typically set at .05
–
–
if you set alpha at .05, you will incorrectly reject the null hypothesis only
5% of the time or less
i.e., you will only conclude 5% of the time that there is a relationship in
the population, when there really is not a relationship
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Hypothesis Testing
•
Steps of hypothesis testing
4. input the data into a statistical program, such as SPSS or
SAS and run the appropriate statistical test

critical region
–
the area on a null hypothesis sampling distribution where the observed
value of the statistic, if it fell in this area, would be considered a rare
event
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Hypothesis Testing
•
Steps of hypothesis testing
5.
make a decision

if result of test statistic is unlikely to occur by chance (that is, if the p value
is less than the alpha level), reject the null hypothesis
p value (probability value)

–
the likelihood of the observed value (or a more extreme value) of a statistic, if the
null hypothesis were true
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Hypothesis Testing
•
Steps of hypothesis testing
6. compute effect size, interpret findings, and make judgment
of practical significance of results

many different effect size indicators
–

Cohen’s d, eta squared (η2), omega squared (ω2), and the amount of
variance explained by one or more independent variables
practical significance
–
claim made when a statistically significant finding seems large enough to
be important
• i.e., whether the difference between the means or the observed
• relationship is “big enough to matter” for practical decisions
• e.g., to continue the line of research, to make policy decisions, or to
make clinical recommendations
– statistically significant results are not always practically significant
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.
Hypothesis Testing
• Directional alternative hypotheses
– an alternative hypothesis that includes a “less than sign” (<)
or a “greater than sign” (>)
 i.e., the researcher wants to test the hypothesis that one population
mean is greater than (or less than) another
– example
 null hypothesis: H0: μTraining ≤ μNo Training
 alternative hypothesis: H1: μTraining > μNo Training
– advantage
 increases statistical power
– disadvantage
 cannot reject null if effect is opposite of prediction
– typically not used in practice even when researcher believes
there is direction to their hypothesis
Research Methods, Design, and Analysis, Twelfth Edition
Christensen • Johnson • Turner
Copyright ©2014 by Pearson Education, Inc.
All rights reserved.